Fair allocation based on two criteria: A DEA game view of ‘Add them up and divide by two’

The phrase ‘add them up and divide by two (Tashite Ni De Waru, in Japanese)’ is an established maxim in Japanese society, and has its historical roots in Japanese culture. This means adopting a middle course between two competing proposals in order to avoid a conflict.In the spirit of Max Weber (1949), this paper establishes a systematically correct scientific proof of ‘add them up and divide by two’ (Add-Div), by using conceptions of the two OR methodologies, data envelopment analysis (DEA) and cooperative game theory. More specifically, in the DEA game scheme of Nakabayashi and Tone (2006), we study an allocation problem with two criteria, in which game-theoretic solutions such as the Shapley value and the nucleolus prove coincident with the result of the Add-Div method. While today some brilliant minds may propose that people should abandon the Add-Div mentality, this paper enables one to re-consider the concept of Add-Div not only as a matter of mentality but also as an application of OR methods. We also illustrate the use of the Add-Div concept where the ‘assurance region’ (AR) method of DEA is incorporated.